Dynamo effect in decaying helical turbulence

Abstract

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity-regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t −1/2 . This is even slower than in the fully helical case, where it decays like t −2/3 . In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity, is approximately constant. This scaling of magnetic energy persists over long time scales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a cross-over to the t −2/3 decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.

Can the Local Bubble explain the radio background?

“…For decaying turbulence and an initially weak magnetic field, we expect magnetic field amplification up to an equilibrium with the kinetic energy (Brandenburg et al 2019). This growth phase may last several initial crossing (turnover) times, up to perhaps ten crossing times, depending on the initial field strength.…”

“…Following the experimental data on the fieldâȂŹs geometry, we set the 85 per cent largest modes to zero. This is a reasonable approximation for decaying turbulence in the case of initially weak magnetic fields that were amplified by a strong driving event (Brandenburg et al 2019), e.g., the sloshing following an off-centre supernova explosion (Krause et al 2014). The magnetic field geometry is discussed further in Sect.…”

Decaying turbulence and magnetic fields in galaxy clusters

“…In the absence of sustained turbulent driving, these helical fields are also expected to decay. While this has been studied for non-helical, subsonic turbulent driving (e.g., Bhat et al 2014;Brandenburg et al 2019), a systematic analysis of free decay of helical magnetic fields in transonic and supersonic turbulence still remains to be performed.…”

The art of simulating the early universe. Part I. Integration techniques and canonical cases

“…Only in this way, we will achieve a certain robustness in the predictions of the potentially observational implications from non-linear high energy phenomena. Furthermore, the techniques developed for studying nonlinear dynamics of classical fields are common to many other non-linear problems in the early universe, like the dynamics of phase transitions [74,75,102,[195][196][197][198][199] and their emission of gravitational waves [200][201][202][203][204][205][206], cosmic defect formation [114,159,[207][208][209][210][211][212][213][214], their later evolution [160-166, 215, 216] and gravitational wave emission [114,167,168,217], axion-like field dynamics [172,175,[218][219][220][221], moduli dynamics [222,223], etc. These techniques can also be used in applications of interest not only to cosmology, but also to other high energy physics areas.…”

“…This can be useful to describe scenarios where a classical scalar field, playing the role of an order parameter in a phase transition, is coupled to a relativistic fluid by means of a phenomenological friction term. This is the basis to describe numerically the dynamics of first order phase transitions [74,75,102,[195][196][197][198][199] and their emission of gravitational waves [200][201][202][203][204][205][206].…”